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What if the creators of a new cryptocurrency gave out new units of the cryptocurrency in exchange for shares of a stock or bond index fund, held these shares in reserves, and allowed owners of the cryptocurrency to redeem them back for shares in the index fund? Wouldn't this effectively peg the cryptocurrency to such a fund?

Wouldn't such a system offer a lot of stability, desperately needed in today's most popular cryptocurrencies?

What kind of issues would the creators or the consumers of the cryptocurrency run into with such a system?

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There are already cryptocurrencies that are backed 1:1 by dollar, see Tether and USDC, or even backed with gold, see Paxos Gold, and yes all of that are redeemable. there is no problem with it so far.

There may be some trust problem, are the issuer really back the cryptocurrency with real asset? (this can solved easily by external auditing though) At 2018 there are some issues that tether aren't pegged 1:1 with USD, the result is Tether value are decreasing to around 0.9 USD. Weirdly enough, even without an external audit(they never got an audit since that scandal), people still believe in tether and the price of tether jumped out to 1 USD Again.

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